Wolfram’s mathworld (http://mathworld.wolfram.com/Dense.html) tells that (in this case) a set is dense if union of that set and the set of its limit point is the real line.

Hence, it is sufficient to show that for every rational number there is a a sequence of irrational numbers the rational number is the limit point of.

So let r be a rational number and i an arbitrary irrational number. Now for all natural numbers n it is true that (r+i)/n is irrational (show by easy induction if necessary).

The above generates a monotonous and limited sequence, hence it has a limit value (given that closed interval [r, i] or [i, r] is perfect). It follows that r is this limit value.

Since the above applies to all r, it follows that irrationals are dense within reals.

Tommi’s last blog post..Classifying good rules

I don’t have much stuff on here that I think’s particularly good, but I went ahead and submitted 3 posts anyways.

Open Game Table is the project I started on Sunday… bizarre.. it’s like our blogger hive mind was working overtime. I only wish I had time to contribute to both projects… maybe I’ll submit my Caretaker creep. or some template conversions I put together..

btw — any plans to submit something to the RPG Bloggers Anthology?

Jonathan’s last blog post..Open Game Table: The 2008 Anthology of Roleplaying Game Blogs